The invention relates to a measuring device for detecting a differential angle of rotation or torque of a torsionally stressed machine part. Such a known measuring device has two bodies of electrically conductive, non-magnetic work material which are arranged coaxially relative to a shaft, one of which bodies being connected with the shaft so as to be fixed for joint rotation therewith, the other body being rotatable relative to the shaft. Moreover, a coil is provided coaxially relative to the shaft and is arranged in the immediate vicinity of the two bodies, high-frequency alternating current passes through the coil. These two bodies comprise cut out portions whose mutual overlapping surface changes as the torsion angle occurring between the bodies increases, wherein the relative rotation of the two bodies can be detected for the purpose of measuring the change in impedance of the coil which occurs as a result of eddy currents induced in the bodies. This known device is relatively costly (DE-PS 29 51 148).